Former Missouri Governor Jay Nixon (L) talks with current Cleveland Browns general manager John Dorsey (center) and Rams general manager Les Snead (R) before the start of the annual Governor's Cup on September 3, 2015 at the Edward Jones Dome in St. Louis. File photo by Bill Greenblatt/UPI | License Photo

Dorsey told NFL Network's Steve Wyche on Wednesday that he hasn't "even told [his] wife" which player the Browns will select with the first overall pick in the draft come Thursday night in Arlington, Texas.

The general manager also acknowledged that Cleveland has not received a legitimate trade offer for that pick.

Dorsey didn't confirm to Wyche that the team will take a quarterback with its first pick. The Browns are mulling between Wyoming quarterback Josh Allen and reigning Heisman Trophy winner Baker Mayfield out of Oklahoma, multiple media outlets reported this week.

Cleveland also holds the No. 4 overall pick of the draft by virtue of a trade with the Houston Texans last year.

The Browns, who limped to a 0-16 mark last year and are 1-31 in the last two seasons, haven't fared well when selecting a quarterback with their first-round pick. Since 1999, the team has chosen the following: Kentucky's Tim Couch (No. 1 overall, 1999), Notre Dame's Brady Quinn (No. 22 overall, 2007), Oklahoma State's Brandon Weeden (No. 22 overall, 2012) and Texas A&M's Johnny Manziel (No. 22 overall, 2014).

Listed at 6-foot-5, 237 pounds, Allen ran the 40-yard dash at the NFL Scouting Combine in 4.75 seconds with a 33 1/2-inch vertical jump. Rang said the knock on Allen is his completion percentage.

Mayfield recently visited with the Browns, with Dorsey referring to the 23-year-old as a "pleasant fella" during his Thursday news conference.

Mayfield passed for 4,627 yards and accounted for 48 touchdowns with just six interceptions while leading Oklahoma to the College Football Playoff last season.

While that is impressive, Mayfield is also linked to some less-than-stellar moments.

Mayfield planted the Sooner flag at midfield after winning at Ohio State and taunted Kansas fans as well. Those actions were preceded by a Feb. 25 arrest in Fayetteville, Ark., on charges of public intoxication, disorderly conduct, resisting arrest and fleeing, which resulted in a plea deal.

Tyrod Taylor, who was the Buffalo Bills' primary quarterback over the last three seasons, was acquired by the Browns in the offseason. The 28-year-old Taylor played in 15 games for the Bills last year and completed 62.6 percent of his passes for 2,799 yards and 14 touchdowns with four interceptions.